Module « numpy.random »

Fonction noncentral_chisquare - module numpy.random

Signature de la fonction noncentral_chisquare

Description

noncentral_chisquare.__doc__

        noncentral_chisquare(df, nonc, size=None)

        Draw samples from a noncentral chi-square distribution.

        The noncentral :math:`\chi^2` distribution is a generalization of
        the :math:`\chi^2` distribution.

        .. note::
            New code should use the ``noncentral_chisquare`` method of a ``default_rng()``
            instance instead; please see the :ref:`random-quick-start`.

        Parameters
        ----------
        df : float or array_like of floats
            Degrees of freedom, must be > 0.

            .. versionchanged:: 1.10.0
               Earlier NumPy versions required dfnum > 1.
        nonc : float or array_like of floats
            Non-centrality, must be non-negative.
        size : int or tuple of ints, optional
            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
            ``m * n * k`` samples are drawn.  If size is ``None`` (default),
            a single value is returned if ``df`` and ``nonc`` are both scalars.
            Otherwise, ``np.broadcast(df, nonc).size`` samples are drawn.

        Returns
        -------
        out : ndarray or scalar
            Drawn samples from the parameterized noncentral chi-square distribution.

        See Also
        --------
        Generator.noncentral_chisquare: which should be used for new code.

        Notes
        -----
        The probability density function for the noncentral Chi-square
        distribution is

        .. math:: P(x;df,nonc) = \sum^{\infty}_{i=0}
                               \frac{e^{-nonc/2}(nonc/2)^{i}}{i!}
                               P_{Y_{df+2i}}(x),

        where :math:`Y_{q}` is the Chi-square with q degrees of freedom.

        References
        ----------
        .. [1] Wikipedia, "Noncentral chi-squared distribution"
               https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution

        Examples
        --------
        Draw values from the distribution and plot the histogram

        >>> import matplotlib.pyplot as plt
        >>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000),
        ...                   bins=200, density=True)
        >>> plt.show()

        Draw values from a noncentral chisquare with very small noncentrality,
        and compare to a chisquare.

        >>> plt.figure()
        >>> values = plt.hist(np.random.noncentral_chisquare(3, .0000001, 100000),
        ...                   bins=np.arange(0., 25, .1), density=True)
        >>> values2 = plt.hist(np.random.chisquare(3, 100000),
        ...                    bins=np.arange(0., 25, .1), density=True)
        >>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob')
        >>> plt.show()

        Demonstrate how large values of non-centrality lead to a more symmetric
        distribution.

        >>> plt.figure()
        >>> values = plt.hist(np.random.noncentral_chisquare(3, 20, 100000),
        ...                   bins=200, density=True)
        >>> plt.show()